WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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For the next lesson, we are going to go over two events that are disjoint.
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Two events are disjoint when those two events cannot occur at the same time.
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It can't happen; it is not possible.
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If we have two events A and B, then the probability or the chance that both are going to occur is 0.
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That means there is no chance for them to occur together.
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It is as if I look at my two events, event A occurring, let's say it is that right there.
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Event B occurring would be like that; they don't overlap.
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That means they cannot happen together; they cannot occur at the same time.
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An example of this, if I were to say that right now, it is 5 o'clock pm.
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It is 5pm; let's say this is A; event A.
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Event B, if I say it is early in the morning.
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See how event A, this statement here, it is 5pm, and in statement B, it is early in the morning.
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They cannot occur at the same time.
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It is not possible for it to be 5pm and for it to be early in the morning.
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These two events would be disjoint.
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These are considered disjoint events because they cannot occur at the same time.
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They cannot occur together.
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If I were to say the same statement here, it is 5 o'clock pm.
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For my second event, my second statement, I am going to say it is dinnertime.
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This is possible; you can have dinner at 5 o'clock pm.
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In this case, probability of A and B would be not disjoint because this can occur at the same time.
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It is not disjoint.
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If two events cannot occur at the same time, they are disjoint.
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If they can, then it is not disjoint.
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Determine if each pair of events is disjoint or not disjoint.
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The first one, statement A, Samantha is more than 10 years old.
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That means she could be 11, 12 years old, 13, 20, 30.
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She is older than 10.
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Statement B, Samantha is less than 8 years old.
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She can't be older than 10 and less than 8.
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This is not possible; this would be disjoint.
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The second one, the first statement, John is 6 feet tall.
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For B, John is between 5'10 and 6'2.
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This is possible; 6 feet is between 5'10 and 6'2; this is not disjoint.
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The next example, a box weighs 10 pounds.
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Name a pair of events that would make this statement disjoint and another pair that is not disjoint.
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We are going to create our own disjoint events and then another pair of events that would be not disjoint.
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That makes sense; that could occur.
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The first statement, the one that is disjoint, let's make it that statement right there.
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A, my first one, a box weighs 10 pounds.
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For B, our second statement, to make it disjoint, the same box weighs less than 8 pounds.
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It wouldn't make sense; this is disjoint.
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For not disjoint, I can say my first statement, a box weighs more than 9 pounds.
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For my next statement, a box weighs less than 11 pounds.
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This is true; these two statements are true; it is not disjoint.
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The third example here, determine if each set of events is independent, dependent, or disjoint.
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Remember independent events, when we have two events that do not affect each other.
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The outcome of the second event is not affected or does not depend on the first event.
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Dependent events are the opposite.
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The second event is affected by the first event.
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The probability of the second event occurring is affected or is determined by the outcome of the first event.
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Disjoint remember is when we have two events that cannot occur at the same time.0713.2.
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It is not possible for them.
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The first statement, a person picks a card from a deck of playing cards.
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Without replacing it, another person picks another card from the same deck.
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There are 52 cards in a deck; a person picks a card.
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That is the first event; the first pick is the first event.
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Without replacing it, another person picks another card from the same deck.
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For the first event, when you pick a card, it is 1 card out of a total of 52.
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This is the first event.
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Then for the second event, for the second pick,
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since the first card is not replaced back into the deck, there is o1ne card missing now.
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There is no longer 52 cards.
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The second person is going to pick 1 card out of a total of 51.
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1 card out of 52 times 1 card out of 51.
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Here all we want to know is if the two events together, is it independent, dependent, or disjoint?
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See how the second event here is affected by this first event because the card was not replaced.
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It is not put back in; so now there is less cards.
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The card that the second person picks might be different; it is affected.
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This would be a dependent event; these are dependent events.
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The second one, Sarah received 100 percent on her chapter five math test.
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Sarah failed her chapter five math test.
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The first event is that she received 100 percent.
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She got an A plus; nothing wrong.
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Then the second event, Sarah failed her chapter five math test.
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If you get 100 percent, is that failing?--no.
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This event here with this event B here cannot occur at the same time.
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It is not possible for both to be true.
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This would be an example of disjoint events.
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The third one, Susan rolled a number cube and got a 4.
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She rolled again and got a 3.
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A number cube is a die; we know that there are 6 sides.
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Each side has a different number; 1, 2, 3.
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She rolled a number cube at got a 4.
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What is the probability of rolling a 4?
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Desired outcome, how many sides on this number cube is a 4?
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Only 1 side; that is 1 out of a total of 6 sides.
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The probability of rolling a 4 is 1/6; that is the first event.
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She rolled again and got a 3; what is the probability of rolling a 3?
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How many sides has a 3?--only 1 side out of 6.
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Here to find the probability of rolling a 4 and then a 3 for those two events is 1/6 times 1/6.
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See how even though she rolled the first time and got a 4, she rolled again.
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For the second event, rolling a 3, was that affected by what she got from the first roll?
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No, just because she rolled a 4 the first time doesn't mean that
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she can't roll a 4 again on the second time, on the second roll.
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These two events are independent.
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This second roll, the second event, is not affected,
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does not depend on this roll here, the probability of getting the 4.
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That is it for this lesson; thank you for watching Educator.com.